This is a graph of 21 ways to melodically move any one tone of the fully-diminished-seventh chord to a tone of a chord that resolves the tension of that fully diminished seventh chord.

A fully-diminished-seventh chord can be resolved in two general ways: (1) so that its root is ‘ti’ leading to ‘do’ as the root in the resolution chord, so the melody sings “ti do”, or (2) so that its fifth is ‘do’ anticipating ‘do’ as the root in the resolution chord, so that, with the resolution, the melody sings “amen”. The first way makes an authentic cadence, and the second way makes a plagal cadence. Since the fully-diminished-seventh chord is symmetrical, you can designate any one of its tones as the root or fifth. This gives you 8 possible resolution root-tones: four tones to end the “ti do”, and four tones to end the “amen”. The resolution chord can be either major or minor, giving you 16 possible resolution-chords.

The tones of the fully-diminished-seventh chord that aren’t singing the first tone of “ti do” or “amen” will, on moving to the resolution chord, fall or rise by either a minor or major second or stay the same. If you’re harmonizing a melody, it’s good to know what chords can be used as the resolution chord, and what tone of the resolution chord (root, third, or fifth) will contain the melody.

Twelve of these resolutions are explained in the next paragraph.

Any tone of the fully-diminished-seventh chord can be resolved upward by a minor second or downward by a major second, to the root, third, or fifth of the minor or major resolution chord. (2x3x2=12)

Six resolutions have you to move the melody upward by a major second or downward by a minor second. They are as follows.

Any tone of the fully-diminished-seventh chord can be resolved upward by a major second or downward by a minor second, to the third of the major chord, fifth of the minor chord, or fifth of the major chord. (2x3=6)

Three resolutions move the melody to the same tone.

Any tone of the fully-diminished-seventh chord can be resolved to the same tone as the root of the minor chord, root of the major chord, or third of the minor chord. (3)

For an example of how to use this chart, let’s say you’re on G#°7, which has the tones, g# b d f, and your main melody is singing the b: if you’re intending to move the b up a minor second to c, then you have six chords to choose from, as indicated* on the chart: Cm, Cmaj, Am, Abmaj, Fm, or Fmaj. If you’re inclined to move the b up a major second, to c#, then, as indicated on the chart, you have three chords to choose from: Amaj, F#m, or F#maj.

* For an upward minor-second, the chart shows six choices, viz., (1) where the tone is the root of the minor chord which in this case is Cm, (2) where the tone is the root of the major chord which in this case is Cmaj, (3) where the tone is the third of the minor chord which in this case is Am, (4) where the tone is the third of the major chord which in this case is Abmaj, (5) where the tone is the fifth of the minor chord which in this case is Fm, and (6) where the tone is the fifth of the major chord which in this case is Fmaj.

The following moves are not on the chart.

You can lower any tone of the fully-diminished-seventh chord by a minor second to make the root of a dominant seventh chord (V7). The V7 can resolve to I, i, VI, or vi. Going through this dominant chord creates a softer landing.

You can raise any tone of the fully-diminished-seventh chord by a minor second to make the minor-7th tone of a half-diminished seventh chord. This chord can act as the iiØ7 of the targeted minor key. The 7th of the iiØ7 wants to fall back a minor second to the 3rd of the dominant chord, V7, which, like in the paragraph above, can be resolved to I, i, VI, or vi.

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